Draft version March 3, 2019Typeset using LATEX twocolumn style in AASTeX62

The Curious Case of KOI 4: Confirming Kepler’s First Exoplanet Detection

Ashley Chontos,1, 2 Daniel Huber,1 David W. Latham,3 Allyson Bieryla,3 Vincent Van Eylen,4, 5

Timothy R. Bedding,6, 7 Travis Berger,1 Lars A. Buchhave,8 Tiago L. Campante,9, 10 William J. Chaplin,11, 7

Isabel L. Colman,6, 7 Jeff L. Coughlin,12, 13 Guy Davies,11, 7 Teruyuki Hirano,14, 1 Andrew W. Howard,15 andHoward Isaacson16

1Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA2NSF Graduate Research Fellow

3Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA4Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08540, USA

5Leiden Observatory, Leiden University, 2333CA Leiden, The Netherlands6Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, NSW 2006, Australia

7Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000, Aarhus C,Denmark

8DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 328, DK-2800 Kgs. Lyngby, Denmark9Instituto de Astrofısica e Ciencias do Espaco, Universidade do Porto, Rua das Estrelas, PT4150-762 Porto, Portugal

10Departamento de Fısica e Astronomia, Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre, s/n, PT4169-007Porto, Portugal

11School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK12NASA Ames Research Center, Moffett Field, CA 94035, USA

13SETI Institute, 189 Bernardo Avenue, Suite 200, Mountain View, CA 94043, USA14Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan

15Department of Astronomy, California Institute of Technology, 1200 E California Boulevard, Pasadena, CA 91125, USA16Astronomy Department, University of California, Berkeley, CA 94720, USA

ABSTRACT

The discovery of thousands of planetary systems by Kepler has demonstrated that planets are ubiq-

uitous. However, a major challenge has been the confirmation of Kepler planet candidates, many of

which still await confirmation. One of the most enigmatic examples is KOI 4.01, Kepler’s first discov-

ered planet candidate detection (as KOI 1.01, 2.01, and 3.01 were known prior to launch). Here we

present the confirmation and characterization of KOI 4.01 (now Kepler-1658), using a combination of

asteroseismology and radial velocities. Kepler-1658 is a massive, evolved subgiant (M? = 1.45 ± 0.06

M, R? = 2.89 ± 0.12 R) hosting a massive (Mp = 5.88 ± 0.47 MJ, Rp = 1.07 ± 0.05 RJ) hot Jupiter

that orbits every 3.85 days. Kepler-1658 joins a small population of evolved hosts with short-period

(≤100 days) planets and is now the closest known planet in terms of orbital period to an evolved star.

Because of its uniqueness and short orbital period, Kepler-1658 is a new benchmark system for testing

tidal dissipation and hot Jupiter formation theories. Using all 4 years of Kepler data, we constrain

the orbital decay rate to be P ≤ -0.42 s yr−1, corresponding to a strong observational limit of Q′? ≥4.826 × 103 for the tidal quality factor in evolved stars. With an effective temperature Teff ∼6200 K,

Kepler-1658 sits close to the spin-orbit misalignment boundary at ∼6250 K, making it a prime target

for follow-up observations to better constrain its obliquity and to provide insight into theories for hot

Jupiter formation and migration.

Keywords: planets and satellites: individual (KOI 4.01), hot Jupiter — stars: individual (Kepler-

1658), fundamental parameters, oscillations — techniques: asteroseismology, photometry,

spectroscopy — Kepler — planetary systems

Corresponding author: Ashley Chontos achontos@hawaii.edu

2

1. INTRODUCTION

The Kepler mission (Borucki et al. 2010; Koch et al.

2010; Borucki 2016) revolutionized the field of exoplan-

etary science. Pre-Kepler exoplanet discoveries were bi-

ased towards close-in giant planets (“hot Jupiters”), a

planet type absent from our own solar system. However,

Kepler later revealed that hot Jupiters are in fact rare,

and smaller sub-Neptune sized planets are ubiquitous in

inner planetary systems (Howard et al. 2012; Dressing

& Charbonneau 2013; Petigura et al. 2013; Gaidos &

Mann 2014; Morton & Swift 2014; Silburt et al. 2015).

When the Kepler spacecraft launched in March 2009,

three planets in the Kepler field were already known

from ground-based transit observations (O’Donovan

et al. 2006; Pal et al. 2008; Bakos et al. 2010). These

targets were designated the first three KOI (Kepler Ob-

ject of Interest) numbers, making KOI 4.01 Kepler’s

first new planet candidate (PC). The initial classifica-

tion in the Kepler Input Catalog (KIC, Brown et al.

2011) for KOI 4 implied a 1.1 solar radius (R) main-

sequence star with an effective temperature (Teff) of

6240 K (Brown et al. 2011). Based on a primary transit

depth of 0.13%, this stellar classification implied that

KOI 4 is orbited by a Neptune-sized planet. However,

because a deep secondary eclipse was observed, KOI

4.01 was marked as a false positive (FP) in early Kepler

KOI catalogs, since a secondary eclipse would not be

observable for a Neptune-sized planet orbiting a main

sequence star.

The NASA Exoplanet Archive reveals a more detailed

picture of the complex vetting history of Kepler’s first

exoplanet candidate. KOI 4.01 was not listed in the

first KOI catalog (Borucki et al. 2011a) but appeared as

a ‘moderate probability candidate’ in the second KOI

catalog (Borucki et al. 2011b), with the host star noted

as a rapid rotator (v sin i = 40 km s−1). In the third cat-

alog, Batalha et al. (2013) listed KOI 4.01 as a PC but it

was marked back to a FP in the fourth catalog (Burke

et al. 2014), likely due to the secondary eclipse. The

fifth (Rowe et al. 2015) and sixth (Mullally et al. 2015)

catalogs did not disposition existing KOIs within cer-

tain parameter spaces. The seventh catalog (Coughlin

et al. 2016) was the first fully uniform catalog using the

Robovetter pipeline, marking 237 KOIs that were previ-

ously FPs back to PCs using updated stellar parameters,

including KOI 4. In the final catalog (Thompson et al.

2018), the Robovetter also dispositioned it as a PC. Un-

til now, Kepler’s first new planet candidate has awaited

confirmation as a genuine planet detection.

Systems like KOI 4.01 are interesting because giant

planets at short orbital periods (P < 100 days) are rare

around subgiant stars (e.g. Johnson et al. 2007, 2010;

Figure 1. Kepler photometry and radial velocity obser-vations for KOI 4.01. Long-cadence photometric data areshown in dark gray while short-cadence are shown in lightgray. Three high-resolution spectra (red points) were ini-tially taken of KOI 4.01 during the mission before it wasmarked as a false positive. This was followed by a break of7 years before it was re-observed by our team in 2017.

Reffert et al. 2015; Lillo-Box et al. 2016; Veras 2016),

although the reason for this is still a topic of debate.

On one hand, this may be related to the stellar mass.

Subgiant host stars are thought to be more massive than

main sequence stars targeted for planet detection. A

higher mass could shorten the lifetime of the protoplan-

etary disk and lead to fewer short-period giant planets

orbiting these type of stars (e.g. Burkert & Ida 2007;

Kretke et al. 2009). Other authors have suggested that

subgiants have fewer short-period planets because these

objects may get destroyed by tidal evolution, which is

likely stronger for more evolved stars (e.g. Villaver &

Livio 2009; Schlaufman & Winn 2013). Distinguishing

between those scenarios is further complicated by the

fact that it is challenging to derive stellar masses of

evolved stars (Lloyd 2011, 2013; Johnson et al. 2013;Ghezzi et al. 2018).

Here we confirm and characterize KOI 4.01, hereafter

Kepler-1658, using a combination of asteroseismology

and spectroscopic follow-up observations. Due to its

short orbital period, Kepler-1658 b is an ideal target

to constrain the role of tides around more evolved stars.

In addition, we are able to constrain the stellar mass

and other stellar parameters to high precision and accu-

racy by analyzing the stellar oscillations and comparing

these to stellar models. We conclude by discussing fu-

ture observations that could provide insight for theories

of hot Jupiter formation and migration.

2. OBSERVATIONS

2.1. Kepler Photometry

The Kepler spacecraft had two observing modes: long-

cadence (29.4 min; Jenkins et al. 2010) and short-

3

Table 1. TRES Radial Velocity Observations

Time (BJD TDB) Phase1 RV (m s−1) σRV (m s−1) BS2 (m s−1) σBS (m s−1)

2455143.566982 39.757 -648.64 261.20 -11.1 205.7

2455343.873508 91.793 -344.33 223.72 -22.9 138.1

2455345.873597 92.313 -1542.39 153.02 244.2 72.1

2457914.843718 759.687 0.00 155.26 -114.2 41.6

2457915.936919 759.971 -756.57 165.32 -122.5 64.7

2457916.865409 760.212 -1391.09 159.21 220.9 58.9

2457917.929198 760.488 -1031.39 103.84 -5.9 70.9

2457918.888799 760.738 -480.41 155.26 -87.2 52.9

2457919.869505 760.992 -1095.83 109.08 108.9 59.6

2457920.859134 761.250 -1458.12 187.52 238.5 95.2

2457960.932038 771.660 -679.80 156.99 -40.2 136.6

2457961.930294 771.919 -891.62 232.50 26.1 127.6

2457965.808860 772.927 -977.16 131.20 -142.2 61.5

2457993.735605 780.182 -1424.46 200.28 21.1 96.0

2457994.753312 780.446 -1205.20 190.75 168.0 50.2

2457999.668199 781.723 -48.17 137.98 -223.2 68.9

2458001.720710 782.256 -971.08 146.58 -48.9 89.2

2458002.718939 782.515 -640.20 127.69 -98.9 60.0

2458003.661261 782.760 -118.49 103.28 -274.6 85.1

2458006.701108 783.550 -873.64 137.11 66.8 77.7

2458007.747359 783.822 -578.74 130.97 -45.6 66.9

2458008.800582 784.095 -1439.71 156.00 -6.5 74.5

2458009.717813 784.333 -1611.87 145.55 149.4 40.9

Notes —1 Indicates the orbital phase of the planet at the time of observation (where 0 phase is defined as the start of Kepler).2 Line bisector spans and uncertainties, as discussed in Section 2.3.

cadence (58.85 s; Gilliland et al. 2010a). In the nom-

inal Kepler mission most Kepler targets were observed

in long-cadence, while 512 short-cadence slots remained

for select targets. Short-cadence observations are impor-

tant for asteroseismology of dwarfs and subgiants, whose

oscillations occur on timescales faster than 30 minutes

(Gilliland et al. 2010b; Chaplin & Miglio 2013).

Decisions on which targets to observe in short-cadence

were made on a quarter-by-quarter basis. In particu-

lar, once planet candidates were detected and assigned

a KOI number, targets were put on short-cadence if the

probability of detecting oscillations was deemed signifi-

cant (Chaplin et al. 2011a). Kepler-1658 was observed

in long-cadence for most of the mission aside from 3

quarters, while it was only observed in short-cadence in

Quarters 2, 4, 7, and 8, for a total of 213.7 days (Figure

1).

2.2. Imaging

Kepler-1658 was observed by Robo-AO, a robotic,

visible light, laser adaptive optics (AO) imager that

searched for nearby companions which could poten-tially contaminate target light curves (Law et al. 2014;

Baranec et al. 2016; Ziegler et al. 2017). Law et al.

(2014) reported a nearby companion to Kepler-1658 at

a separation of 3.42” and a contrast of 4.46 mag in the

LP600 filter, which has a similar wavelength coverage

to the Kepler bandpass. In addition to Robo-AO, the

Kepler UKIRT survey reported a detection of the same

companion with a contrast of 4.23 ∆mag in the J-band

(Furlan et al. 2017). Gaia Data Release 2 reported par-

allaxes of 1.24 ± 0.03 mas and 0.75 ± 0.05 mas corre-

sponding to Kepler-1658 and its companion, respectively

(Lindegren et al. 2016). Therefore, we conclude that the

two targets are not physically associated.

2.3. Spectroscopy and Radial Velocities

4

Initial spectroscopic follow-up of Kepler-1658 was ob-

tained by the Kepler Follow-up Observing Program

(KFOP), including the HIRES spectrograph (Vogt

et al. 1994) on the 10-m telescope at Keck Obser-

vatory (Mauna Kea, Hawaii), the FIES spectrograph

(Djupvik & Andersen 2010) on the 2.5-m Nordic Opti-

cal Telescope at the Roque de los Muchachos Observa-

tory (La Palma, Spain), and the Tillinghast Reflector

Echelle Spectrograph (TRES) (Furesz 2008) on the 1.5-

m Tillinghast reflector at the F. L. Whipple Observatory

(Mt. Hopkins, Arizona). The observing notes archived

at the Kepler Community Follow-up Observing Pro-

gram (CFOP)1 show that these spectra confirmed that

Kepler-1658 is a rapid rotator which, combined with the

detection of the close companion (see previous section),

discouraged further follow-up observations to confirm

the planet candidate.

Following the asteroseismic reclassification of the host

star (see next section), we initiated an intensive radial-

velocity follow-up program using TRES, a fiber-fed

echelle spectrograph spanning the spectral range 3900-

9100 Angstroms with a resolving power of R∼44,000.

We obtained 23 spectra with TRES between UT Novem-

ber 08 2009 and September 13 2017 using the medium

2.3” fiber. The spectra were reduced and extracted

as outlined in Buchhave et al. (2010). The average

exposure time of ∼1800 seconds, corresponding to a

mean signal-to-noise (S/N) per resolution element of

∼53 at the peak of the continuum near the Mg b triplet

at 519nm. We used the strongest S/N spectrum as

a template to derive relative radial velocities by cross-

correlating the remaining spectra order-by-order against

the template, which is given a relative velocity of 0 km

s−1, by definition.

Monitoring of standard stars with TRES shows that

the long-term zero point of the instrument is stable to

within ± 5 m s−1 over recent years. Due to mechanical

and optical upgrades to TRES in the early years, there

were major shifts in the instrumental zero point of the

velocity system. The correction for the 2009 observa-

tion was -115 m s−1 and the correction for both 2010

observations was -82 m s−1.

A bisector analysis was performed on the TRES spec-

tra as described in Torres et al. (2007) to check for asym-

metries in the line profile which could be indicative of

an unresolved eclipsing binary. The line bisector spans

(BS) showed no correlation with the measured radial

velocities and are small compared to the orbital semi-

1 https://exofop.ipac.caltech.edu/kepler/

Table 2. Stellar Parameters

Parameter KIC 3861595

Basic Properties

2MASS ID 19372557+3856505

Right Ascension 19 37 25.575

Declination +38 56 50.515

Magnitude (Kepler) 10.195

Magnitude (V ) 11.62

Magnitude (TESS) 10.98

Spectroscopy

Effective Temperature, Teff (K) 6216± 78

Metallicity, [m/H] −0.18± 0.10

Projected rotation speed, v sin i (km s−1)∗ 33.95± 0.97

Asteroseismology

Stellar Mass, M? (M) 1.447± 0.058

Stellar Radius, R? (R) 2.891+0.130−0.106

Stellar Density, ρ? (g cm−3) 0.0834± 0.0079

Surface Gravity, log g (dex) 3.673± 0.026

∗ Using FIES spectrum, discussed in Section 3.3.

amplitude. All relative velocities, bisector values, and

associated uncertainties are listed in Table 1.

3. HOST STAR CHARACTERIZATION

3.1. Atmospheric Parameters

Atmospheric parameters were derived from the TRES

and FIES spectra using the Stellar Parameter Classifica-

tion code (SPC, see Buchhave et al. 2012). We adopted

a weighted mean of the solutions to the individual spec-

tra, yielding Teff = 6216 ± 51 K, log g = 3.57 ± 0.1 dexand [m/H] = −0.18±0.08 dex. The SPC-derived log g is

in good agreement with the asteroseismic detection (see

below), and thus no iterations between the spectroscopic

and asteroseismic solution were required.

We also analyzed the HIRES spectrum using Specmatch-

emp (Yee et al. 2017), yielding consistent values within

2σ (Teff = 6241 ± 110 K, [m/H] = −0.05 ± 0.09 dex).

We adopted the weighted SPC values as our final solu-

tion, and added 59 K in Teff and 0.062 dex in [m/H] in

quadrature to the formal uncertainties to account for

systematic differences between spectroscopic methods

(Torres et al. 2012). The final adopted values are listed

in Table 2.

3.2. Asteroseismology

Asteroseismology, the study of stellar oscillations, and

transits form a powerful synergy to investigate exoplanet

5

Figure 2. Power spectrum of the Kepler short-cadencedata for Kepler-1658. Top: Power spectrum in log-log scale,where the region of oscillations is marked by the dashed lines.The original power is shown in gray and smoothing filters ofwidths 0.5 and 2.5 µHz are shown in black and red, respec-tively. Bottom: Power spectrum in linear space zoomed inon the region of oscillations. The shaded area highlights thepower that is used to calculate the autocorrelation, shown inthe inset.

systems. (Stello et al. 2009b; Gilliland et al. 2010b; Hu-

ber et al. 2013a; Van Eylen et al. 2014; Huber 2015).Currently, more than one hundred Kepler exoplanet

host stars have been characterized through asteroseis-

mology (Huber et al. 2013a; Lundkvist et al. 2016).

We performed a search for oscillations in Kepler-1658

in the Kepler short-cadence data. Asteroseismic anal-

ysis included removing any data with nonzero quality

flags, clipping transits and outliers, then normalizing

each individual quarter before concatenating the light

curve. A high-pass filter was used to remove long-period

systematics before computing the power spectrum. Box

filters of widths 0.5 and 2.5 µHz were used to smooth the

power spectrum in order to make the signal clear. The

power spectrum for Kepler-1658 can be seen in Figure 2,

showing a characteristic frequency-dependent noise due

to granulation and a power excess marked by the gray

dashed lines. We note that the strong peak near ∼300

Figure 3. Surface gravity versus effection temperature forconfirmed Kepler exoplanet hosts. Gray points representconfirmed hosts, with known asteroseismic hosts in black.Kepler-1658, represented by the red star, sits in an underpop-ulated area of stellar parameter space as a massive, evolvedsubgiant.

µHz is a well-known artefact of Kepler short-cadence

data (Gilliland et al. 2010a).

Since the power excess has relatively low S/N, we used

an autocorrelation to confirm the oscillations. The re-

gion with excess power should have a width that we can

estimate by using a linear scaling relation:

w = w

(νmax

νmax,

), (1)

where w = 1300 µHz is the width of oscillations in the

Sun. To prevent adding noise to the calculated autocor-

relation, only the power in this region was used. Con-

firming the oscillations requires detecting peaks with a

regular spacing that follows the well-known correlation

between ∆ν and νmax (Stello et al. 2009a; Hekker et al.

2009; Mosser et al. 2010; Hekker et al. 2011a,b; Huber

et al. 2011). The autocorrelation of the power spectrum

is shown in the inset in Figure 2 and confirms the de-

tection of oscillations. Red and blue dashed lines mark

the expected positions of regular spacings based on as-

teroseismic scaling relations. Red is the expected spac-

ing of adjacent radial and dipole modes (∼n∆ν/2) and

blue is the expected spacing of consecutive radial modes

(∼n∆ν).

The low S/N of the seismic detection, combined with

the possible presence of mixed modes, make the autocor-

relation an imprecise tool to measure ∆ν. Additionally,

the short-cadence artefact at ≈ 300µHz prevents a re-

liable background fit to the power spectrum and thus

6

Figure 4. Top: Transit-clipped Quarter 11 long-cadencelight curve for Kepler-1658. Bottom: Lomb-Scargle peri-odogram showing a strong peak at 5.66 ± 0.31 days, whichwe interpret as the stellar rotation period.

a measurement of νmax. To determine ∆ν, we com-

puted echelle diagrams over a grid of trial ∆ν values

separated by 0.1µHz to identify the spacing which pro-

duces straight ridges of modes of consecutive overtones,

a method commonly adopted to verify the accuracy of

∆ν values (Bedding et al. 2010). We identified 32.5µHz

as the correct spacing, consistent with four independent

analyses by co-authors (Campante et al. 2010; Chap-

lin et al. 2011b; Bedding 2012; Davies et al. 2016). We

adopted the result from the manual analysis as our final

value and adopted the scatter over all methods as anuncertainty, yielding ∆ν = 32.5± 1.6µHz.

Since the low S/N does not allow a reliable constraints

on individual frequencies or νmax, we used grid-based

modeling (Gai et al. 2011) with atmospheric parameters

from spectroscopy and the asteroseismic ∆ν to derive a

full set of host star properties. To perform grid-modeling

we used the open-source code isoclassify1 (Huber

et al. 2017), which adopts a grid of MIST isochrones

(Choi et al. 2016) to probabilistically infer stellar pa-

rameters given any combination of photometric, spec-

troscopic or asteroseismic input parameters and adopts

theoretically motivated corrections for the ∆ν scaling

relation from Sharma et al. (2016). The results confirm

that Kepler-1658 is a relatively massive (M? = 1.45 ±

1 https://github.com/danxhuber/isoclassify

-500

0

500

1000

1500

2000

2500

5185 5190 5195 5200 5205 5210

flux

wavelength [angstrom]

Figure 5. One FIES spectral segment of Kepler-1658. Atheoretical, unbroadened spectrum is convolved with rota-tion and a macroturbulent broadening kernel to fit the spec-trum and is shown in red, where the scatter in the residualsof the best-fit v sin i value is shown below the spectrum.

0.06 M) and evolved (R? = 2.89 ± 0.12 R) subgiant

star (Table 2). Kepler-1658 joins a small sample of sub-

giant host stars for which the stellar mass is accurately

determined through asteroseismology (Figure 3).

We note that ∆ν scaling relation is based on simpli-

fied assumptions compared to analyses using individ-

ual mode frequencies, and thus may be affected by sys-

tematic errors. However, independent model calcula-

tions have demonstrated that the relation is accurate to

< 1% in ∆ν (<0.5% in ρ) for stars in the Teff and [m/H]

range of Kepler-1658 (White et al. 2011; Rodrigues et al.

2017). Therefore, any potential systematic error in ρ?introduced by using the ∆ν scaling relation is negligible

compared to our adopted uncertainties.

3.3. Stellar Rotation

The top panel of Figure 4 shows the unfiltered light

curve of Kepler-1658 from Quarter 11, demonstrating

strong evidence for rotational modulation due to spots.

The photometric variability has an amplitude of ∼0.1%

and shows a strong peak at 5.66 ± 0.31 days in the

Lomb-Scargle (LS) periodogram (bottom panel of Fig-

ure 4). We tested for temporal variations of the stellar

rotation by calculating a LS periodogram of the unfil-

tered light curve for each quarter available. The analysis

demonstrated that the equatorial rotation velocity does

not change over the Kepler baseline. Combining this

rotation period with the asteroseismic radius, we com-

pute an equatorial rotation velocity, v = 25.82 ± 1.77

km s−1.

In order to estimate the projected rotation velocity

(v sin i) of Kepler-1658, we analyzed the FIES spectrum

7

using the technique described by Hirano et al. (2012).

In brief, we convolved a theoretical, unbroadened spec-

trum generated by adopting the stellar parameters for

Kepler-1658 (Coelho et al. 2005) with the rotation plus

macroturbulence broadening kernel (and instrumental

profile), assuming the radial-tangential model (Gray

2005). The broadening kernel has several parameters,

including v sin i, the macroturbulent velocity ζ, and stel-

lar limb-darkening parameters, but we only optimized

v sin i, along with the overall normalization parameters

describing the spectrum continuum.

We attempted the fits for three different spectral seg-

ments (5126-5154 A, 5186-5209 A, 5376-5407 A), where

an example of one segment is shown in Figure 5. The

uncertainty of v sin i was derived based on the scatter of

the best-fit values for these segments. For the macrotur-

bulent velocity, we adopted ζ = 4.7± 1.2 km s−1 based

on the empirical relation between Teff and ζ derived by

Hirano et al. (2014), but we found that choice of ζ has

very little impact on the estimated v sin i, due to the

latter’s large value (variation less than 0.2 km s−1). We

found the v sin i for Kepler-1658 to be 33.95 ± 0.97 km

s−1.

There is a clear discrepancy between the equatorial

rotation velocity (v) and projected rotation velocity

(v sin i) we computed, with v sin i v. As discussed

in Section 2.2, there is a companion within the 4” Ke-

pler pixel and is therefore not resolved. As a result,

we tested whether this rotational signal is coming from

Kepler-1658 or from its neighbor using Kepler target

pixel files (TPFs).

Since the angular separation between Kepler-1658 and

its neighbor is the size of a Kepler pixel, we wanted to

identify in which pixel the rotational signal is strongest.

We used the difference imaging technique (Bryson et al.

2013; Colman et al. 2017), which involved phasing the

light curve on the period of the rotational signal, bin-

ning by a factor of 1000, and selecting the data that fell

within ± 1% of the peaks and troughs of the phased light

curve. To create the difference image, we subtracted the

data around the troughs from the data around the peaks.

We did this for each pixel, creating a difference image

which gives an indication of the relative strength of the

rotational signal over the postage stamp. We then com-

pared the difference image to an average image from the

same observing quarter (Figure 6), and found that in

11 of the 17 quarters the pixel with the brightest flux is

the same as the pixel where the rotational signal is the

strongest. Differences in the other 6 quarters did not

exceed one pixel and were inconsistent with the relative

positions of the KOI-4 and the imaged companion (see

Figure 6. Panel (a): Target pixel files of Kepler-1658 av-eraged over one full quarter. Panel (b): A difference imageusing frames coinciding with the maxima and minima of aphase curve calculated from the measured rotation period.The star marks the location of Kepler-1658, and the com-panion identified using AO imaging is marked with a cross.

symbols in Figure 5). These results strongly imply that

the rotational signal is coming from Kepler-1658.

To account for the discrepancy between v and v sin i,

we could introduce a latitudinal differential rotation of

20-40%. According to Collier Cameron (2007), the mag-

nitude of differential rotation for a star with Teff = 6216

K is estimated to be ∆Ω ∼0.28 radian day−1. From the

rotation period of the star, the angular velocity of the

spot is Ω ∼1.1 radian day−1. The observed high v sin i

could be explained if the spot that Kepler observed is

8

0 1 2 3 4 5 6Period (days)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Powe

r

Figure 7. Periodogram of the radial velocity data. The reddashed line marks the period recovered from the light curve.The peak with the same period as the transit light curve hasa false alarm probability of 4.38 × 10−5.

long-lived, located at a relatively high latitude, and its

angular velocity at the equator is ∼1.5 radian day−1.

4. ORBITAL & PLANETARY PARAMETERS

4.1. Confirmation of Kepler-1658 b

An unambiguous confirmation of a transiting exo-

planet is typically performed by detecting radial velocity

variations that are in phase with the ephemeris deter-

mined from transits. The initial three radial velocities

(RVs) were taken as part of the Kepler Follow-up pro-

gram during the Kepler mission. We obtained 20 more

TRES RVs once we realized that it was possible that

Kepler-1658 was hosting a planet (Figure 1), for a total

of 23 RV observations.

As discussed in Section 3.3, Kepler-1658 is rotating

rapidly, thus resulting in RVs with relatively large un-

certainties. Despite this limitation, a periodogram of

the RV data only reveals a highly significant peak that

is fully consistent with the same period of the transit sig-

nal (Figure 7). Additionally, phasing the RVs with the

ephemeris and orbital period from Kepler reveals a clear

variation with a semi-amplitude, K? = 579.45+43.13−42.94 m

s−1, well above the detection threshold set by the RV

uncertainties (Figure 8d). Therefore, the consistency

between the RV and transit data unambiguously con-

firms Kepler-1658 b as a hot Jupiter.

4.2. Transit & RV Modeling

To perform a combined transit and radial velocity fit

we used the TRES measurements in Table 1 and Kepler

long-cadence data, which cover a 4 times longer baseline

than short-cadence data. For computational efficiency,

we only used three times the transit duration centered

Table 3. Model Parameters

Parameter Prior

z U [−1; 1]

u1a N (0.3033; 0.6)

u2a N (0.3133; 0.6)

u1 ≥ 0

u1 + u2 ≤ 1

u1 + 2u2 ≥ 0

γ (m s−1) U [−1200;−700]

K (m s−1) U [350; 850]

P (days) U [3.75; 3.95]

T0 (BKJD)b U [171.9; 173.9]

b U [0; 1]

Rp/R? U [0.02; 0.06]

e sinω U [−1; 1]

e cosω U [−1; 1]

e 1/e

δocc (ppm) U [0; 200]

ρ? (g cm−3)c N (0.0834; 0.0079)

Notes —a Adopted from Claret & Bloemen (2011) archived tables

with additional priors to prevent nonphysical values.b BKJD is the time system used by Kepler and is defined

by Barycentric Julian Date (BJD) – 2454833.c Adopted from the asteroseismic analysis.

at the time of mid-transit for both the primary and sec-

ondary eclipses (Figure 8c).

We modeled the light curve and RV observations us-

ing ktransit1, an implementation of the analytical

model by Mandel & Agol (2002). We assumed a lin-

ear ephemeris (constant orbital period) and quadratic

limb darkening law. The model fitted for the follow-

ing parameters: orbital period (P ), time of mid-transit

(T0), linear (u1) and quadratic (u2) limb-darkening coef-

ficients, mean stellar density (ρ?), systematic RV offset

(γ), eccentricity times the sine of the argument of peri-

astron (e sinω), eccentricity times the cosine of the ar-

gument of periastron (e cosω), occultation depth (δocc),

impact parameter (b), ratio of the planetary radius to

the stellar radius (RP/R?), photometric zero point (z),

and velocity semi-amplitude (K?). The predicted RV

jitter due to stellar variability for a a star like Kepler-

1658 is on the order of a few m s−1 (e.g. Yu et al. 2018),

and thus negligible compared to the formal RV uncer-

tainties (∼ 100− 200 m s−1).

1 https://github.com/mrtommyb/ktransit

9

Figure 8. Simultaneous transit and RV fit through MCMC analysis of Kepler-1658. Panels (a-b): Phase-folded light curvecentered on the primary and secondary transits, where black squares are 10-min bins. The original data points from panel (b)have been removed for clarity. Panel (c): Full phase-folded light curve, where only gray points are used in the MCMC analysis.Panel (d): TRES RV observations. The median value for each parameter is used to generate a model and is shown in red. Onehundred samples are drawn at random and added with transparency to give an idea of the uncertainty in the model.

We used a Gaussian prior of 0.083 ± 0.008 g cm−3

for the mean stellar density derived from asteroseismol-

ogy, as discussed in Section 3.2. Since Kepler-1658 is a

rapid rotator resulting in large RV uncertainties, having

an independent measurement of the mean stellar den-

sity helped break the degeneracies that exist between e

and ω. Using stellar parameters Teff = 6216 K, log g

= 3.57 (dex), and [m/H] = -0.18, we extracted limb-

darkening coefficients u1 = 0.3033 and u2 = 0.3133 from

archived tables (Claret & Bloemen 2011) by using the

nearest grid point. We assigned Gaussian priors for the

limb-darkening coefficients, using the Claret & Bloemen

(2011) values as the center of the distribution with a

width of 0.6. Additional priors on u1 and u2 are im-

plemented, using linear combinations to prevent the pa-

rameters from taking nonphysical values (Burke et al.

2008; Barclay et al. 2015). We used a Jeffreys prior

for eccentricity (1/e) to avoid a positive bias (Eastman

et al. 2013). The remaining parameters were assigned

uniform (flat) priors and are listed in Table 3.

We explored the parameter space by fitting the

planet transit and RV data simultaneously using emcee,

a Markov chain Monte Carlo (MCMC) algorithm

(Foreman-Mackey et al. 2013a). We initialized 30 walk-

ers, each taking 105 steps. A burn-in phase of 4×103

steps was removed from each chain before concatenat-

ing samples to obtain the final posterior distribution

for each parameter. A corner plot is shown in Figure 9

to demonstrate convergence of the 13-dimensional pa-

rameter space, highlighting known correlations in the

parameter space.

4.3. System Parameters

All physical parameters and corresponding uncertain-

ties for Kepler-1658 derived from the joint transit and

RV model can be found in Table 4. In addition to the

transit and RV observations, asteroseismology was crit-

ical to break parameter degeneracies. Specifically, since

Kepler-1658 b has such a short orbital period, an eccen-

tricity, e = 0.06 ± 0.02 initially seemed unlikely but is

required due to the observed transit duration (2.6 hours)

and the strong constraint from the asteroseismic mean

stellar density. A visualization of this can be seen in

Figure 8(a-b), where the time from mid-transit of the

primary and secondary is plotted on the same timescale.

The difference in transit durations and the slight offset

of the secondary eclipse can only be explained by a mild

10

Figure 9. Posterior distributions for 13-dimensional MCMC analysis of the simultaneous transit and RV fit. The parametersacross the bottom are: time of mid-transit (T0), linear (u1) and quadratic (u2) limb-darkening coefficients, eccentricity timesthe cosine of the argument of periastron (e cosω), eccentricity times the sine of the argument of periastron (e sinω), impactparameter (b), occultation depth (δocc), orbital period (P ), mean stellar density (ρ?), ratio of the planetary radius to the stellarradius (RP/R?), velocity semi-amplitude (K?), systematic RV offset (γ), and photometric zero point (z).

11

eccentricity since we have the strong prior constraint on

the mean stellar density from asteroseismology.

Furlan et al. (2017) reported planet radius correction

factors (PRCF) for photometric contamination from

nearby stellar companions. Depending on the separation

and contrast ratio, the companion can contribute to the

total flux throughout the phase of the orbit, including

the primary transit, thus underestimating the radius of

the planet. Since RV observations confirm the planet is

orbiting the primary star, we obtained a final planetary

radius of Rp = 1.07 ± 0.05 RJ using a PRCF = 1.0065%

± 0.0003% (Furlan et al. 2017). We note that this is

PRCF is based on a measured contrast in the LP600 fil-

ter (see Section 2.2), which is commonly assumed to be

similar to the Kepler bandpass (Law et al. 2014; Baranec

et al. 2016; Ziegler et al. 2017). The PRCF was taken

into account before deriving physical planet parameters

and is therefore taken into consideration for the final

values listed in Table 4.

The secondary eclipse allows an estimate of the plan-

etary albedo. According to Winn (2010), a geometric

albedo can be determined by:

Aλ = δocc(λ)

(Rp

a

)−2

, (2)

where δocc is the occultation depth. Using Equation

(2), we derived a geometric albedo of 0.724+0.090−0.081 in the

Kepler bandpass. This value is consistent to within 1-2σ

of RoboVetter’s analysis by Coughlin et al. (2016), which

estimated a value of either 0.494+0.186−0.083 or 0.348+0.145

−0.062,

depending on the lightcurve detrending method used.

Following Winn (2010), the planet inclination can be

derived by:

btra =a cos i

R?

(1− e2

1 + e sinω

), (3)

where btra is the impact parameter b of the primary tran-

sit and a is the planet’s semimajor axis. Using Equation

(3), we obtained an inclination, i = 76.52 ± 0.59o. This

is consistent with the short orbital period and high im-

pact parameter, b = 0.947 ± 0.003.

The inclination of the orbital plane of the planet is

used to break the Mp sin i degeneracy that would other-

wise exist from RV observations alone. Given that Mp

M?, the data determine Mp/M?2/3 through:

Mp

(Mp +M?)2/3=K?

√1− e2

sin i

(P

2πG

)1/3

, (4)

but not Mp itself (Winn 2010). Because asteroseismol-

ogy provides a stellar mass, the planet mass can be de-

termined through Equation (4), yielding Mp = 5.87 ±

Table 4. MCMC Parameter Summary

Parameter Best-fit Median 84% 16%

Fitted Parameters

z (ppm) 1.703 2.350 +1.316 -1.317

P (days) 3.8494 3.8494 +8.04-7 -8.01e-7

T0 (BKJD) 172.9241 172.9241 +1.69-4 -1.67e-4

b 0.9501 0.9471 +0.0025 -0.0032

Rp/R? 0.0359 0.0369 +0.0008 -0.0007

e sinω 0.0580 0.0622 +0.0198 -0.0188

e cosω -0.0081 -0.0084 +0.0008 -0.0008

δocc (ppm) 61.842 62.127 +3.712 -3.750

u1 0.0154 0.1179 +0.1513 -0.0859

u2 0.0453 0.0487 +0.1276 -0.1082

γ (m s−1) -915.88 -929.67 +31.19 -31.26

K (m s−1) 575.80 580.83 +43.13 -42.94

ρ? (g cm−3) 0.1068 0.1130 +0.0063 -0.0060

Derived Parameters

a (AU) 0.0546 0.0544 0.0007 -0.0007

Rp (RJ)∗ 1.04 1.07 +0.05 -0.05

a/R? 4.07 4.04 0.18 -0.17

e 0.0585 0.0628 +0.0197 -0.0185

ω (o) -7.99 -7.73 +1.93 -3.37

Mp (MJ)∗ 5.88 5.88 +0.47 -0.46

ρp (g cm−3) 7.00 6.36 +1.07 -0.91

i (o) 76.55 76.52 +0.58 -0.59

Aλ 0.785 0.734 +0.090 -0.081

∗ Adopting a Jupiter radius of 6.9911 x 104 km and mass

of 1.898 x 1027 kg.

0.46 MJ. Combined with the corrected radius, we find

a bulk density of ρp = 6.36+1.07−0.91 g cm−3.

The mean stellar density modeled from the light curve,

ρ? = 0.113 ± 0.006, converged 3σ higher than the

mean stellar density determined through asteroseismol-

ogy. Analytical solutions for transit models are based

on assumptions that the scaled semi-major axis, a/R?& 8 and the impact parameter, b 1 (Seager & Mallen-

Ornelas 2003; Winn 2010). We speculate that this incon-

sistency is due to the fact that the Kepler-1658 system

falls in a parameter space where these approximations

no longer hold (a/R? ≈ 4, b ≈ 0.95).

5. DISCUSSION

5.1. Orbital Period Decay

Kepler-1658 joins a rare population of exoplanets in

close-in orbits around evolved, high-mass subgiant stars

(Figure 10). One theory for the lack of such planets

12

Figure 10. Confirmed exoplanets taken from the NASA exoplanet archive (accessed on November 7, 2018, with the error barsomitted for clarity) Left: semimajor axis vs. stellar radius, where the dotted line represents R?= a. Of all the evolved stars,Kepler-1658 is the closest short-period planet orbiting an evolved star. Right: semimajor axis vs. stellar mass. Short-periodplanets (≤ 100 days) orbiting evolved stars (≥ 2.5 R) are shown in blue, with values taken from: HD 102956 (Johnson et al.2010), Kepler-56 (Huber et al. 2013b), Kepler-278 and Kepler-391 (Rowe et al. 2014), Kepler-91 (Lillo-Box et al. 2014), Kepler-432 (Ciceri et al. 2015; Quinn et al. 2015), Kepler-435 (Almenara et al. 2015), K2-11 (Montet et al. 2015), HIP 67851 (Joneset al. 2015), 8 UMi (Lee et al. 2015), K2-39 (Van Eylen et al. 2016), K2-97 (Grunblatt et al. 2016), Kepler-637, Kepler-815,Kepler-1004, and Kepler-1270 (Morton et al. 2016), TYC 3667-1280-1 (Niedzielski et al. 2016), K2-132 (Grunblatt et al. 2017),HAT-P-67 (Zhou et al. 2017), KELT-11 (Pepper et al. 2017), WASP-73 (Stassun et al. 2017), and 24 Boo (Takarada et al. 2018).

is tidal evolution, occuring when a close-in giant planet

tidally interacts with its host star (Levrard et al. 2009;

Schlaufman & Winn 2013). Tidal interactions in a 2-

body system are complex, and different driving mecha-

nisms depend on a number of parameters (Zahn 1989;

Barker & Ogilvie 2009; Lai 2012; Rogers et al. 2013).

A system undergoing tidal dissipation conserves total

angular momentum but dissipates its energy, and ulti-

mately the dynamical evolution in the system is deter-

mined by the transfer of angular momentum between ro-

tational and orbital parameters (Zahn 1977; Hut 1981).

There are only two possible outcomes to tidal evolu-

tion, depending on the stability of the system. One is a

stable equilibrium in a coplanar, circular, synchronous

orbit. If the total angular momentum in the system ex-

ceeds a critical value, then the system becomes unstable,

mostly dependent on the moments of inertia of both the

host star and planet. A telltale sign of instability is when

the orbital period of the planet is shorter than the rota-

tional period of the star. When this happens, the planet

deposits angular momentum onto the star, causing the

star to spin up and the orbit to shrink (Levrard et al.

2009; Adams et al. 2010; Schlaufman & Winn 2013; Ble-

cic et al. 2014; Maciejewski et al. 2016; Van Eylen et al.

2016). In this latter scenario, there is no stable equilib-

rium point and the planet will migrate inwards until it

is eventually engulfed by the host star. However, even

systems that are marginally stable can be susceptible to

inward planet migration due to evolutionary effects or

angular momentum loss through magnetized winds (van

Saders & Pinsonneault 2013).

Following Levrard et al. (2009), we can estimate the

timescale of orbital decay using:

τa '1

48

Q′?n

(a

R?

)5(M?

Mp

)(5)

where n is the mean orbital angular velocity and Q′? is

the tidal quality factor, which is a single parameter that

encapsulates physical processes that occur in tidal dissi-

pation. A more recent paper by Lai (2012) suggests that

Q′? can vary for different tidal processes (e.g. orbital de-

cay and spin-orbit alignment). In addition, tidal theory

is very poorly constrained observationally, resulting in

possible values for Q′? that span several orders of mag-

nitude, ranging from 102 to 1010 (Levrard et al. 2009;

Barker & Ogilvie 2009; Adams et al. 2010; Schlaufman &

Winn 2013; Blecic et al. 2014). Therefore, tidal dissipa-

tion timescales remain highly uncertain. Observations

of orbital period decay would provide better constraints

on Q′?, which is currently poorly understood due to the

13

Figure 11. Deviation from a constant orbital period versus epoch for Kepler-1658. Original transit times using Kepler long-cadence data are shown in gray and binned data is shown in black. Our analysis found a tidal quality factor of Q′? = 1.219 ×105, shown by the blue line with 1σ, 2σ, and 3σ levels shown in different transparencies. Theoretical values of Q′? = 103, 5 ×103, 104, and 106 are shown. Our results provide a strong lower limit for the tidal quality factor, ruling out Q′? ≤ 4.826 × 103

for evolved subgiants for the first time observationally.

complex nature of tidal interactions. Orbital period de-

cay of a hot Jupiter was first proposed by Lin et al.

(1996) and was only recently detected in WASP-12b by

Maciejewski et al. (2016). Based on ten years of transit

data, Maciejewski et al. (2016) reported a tidal quality

factor of 2.5 × 105 for a main-sequence (MS) host star.

Patra et al. (2017) use new transit times of WASP-12b

to further confirm evidence of period decay and find a

consistent tidal quality factor of 2 × 105.

For subgiant and giant stars such as Kepler-1658,

Schlaufman & Winn (2013) suggest that the stars be-

come more dissipative as they evolve off the MS, with

Q′? closer to 102-103. Kepler-1658 is a prime target to

constrain orbital period decay because it has a scaled

semi-major axis of a/R? ≈ 4 (Figure 10) and the time

scale of period decay is a sensitive function of this pa-

rameter (Equation 5). There is also evidence that the

Kepler-1658 system is unstable because the orbital pe-

riod of the planet is less than the stellar rotation period.

In order to test for evidence of period decay, we

divided the long-cadence light curves into segments

with a length corresponding to the orbital period, P =

3.85 days. We modeled the individual transits using

ktransit and used a similar MCMC analysis to deter-

mine the transit times. All other parameters were fixed

to the values from the global fit discussed in Section 4.2.

The individual transit times are shown in Figure 11 andlisted in Table 5.

Following Maciejewski et al. (2016), we modeled the

period decay rate by adding a quadratic term to the

previously assumed linear ephemeris:

Tx = T0 + Px+1

2δPx2, (6)

where x is the orbit number, Tx is the time of mid-

transit of x orbit, and δP is the change in orbital pe-

riod between consecutive orbits (PP ). We used MCMC

analysis described by Foreman-Mackey et al. (2013a) to

fit for T0, P , and δP . We placed uniform priors on T0

and δP and a Gaussian prior on P , as derived from the

combined transit and RV fit result.

Our analysis found δP = (-.2048 ± 1.723) × 10−8

days, corresponding to a decay rate of P = (-16.8 ±141.25) ms yr−1, where a negative value is indicative of

14

Table 5. Individual Transit Times

Epoch (BJD) 84% 16%

2454955.88020 0.00176 -0.00174

2454959.72578 0.00121 -0.00116

2454967.43397 0.00112 -0.00118

2454971.28509 0.00158 -0.00154

2454975.12848 0.00131 -0.00130

2454978.97490 0.00132 -0.00125

2454982.82490 0.00173 -0.00179

2454986.67586 0.00152 -0.00152

2454990.52639 0.00138 -0.00129

2454994.37652 0.00196 -0.00198

2455005.92202 0.00189 -0.00191

2455009.77189 0.00129 -0.00126

2455013.62780 0.00333 -0.00284

Note —

This table is published in its entirety on the journal

website in machine-readable format. A portion is shown

for formatting purposes. A version is also available in the

source materials.

orbital decay. This corresponds to an infall timescale of

20 Myr. For consistency and comparison to the values

reported in Maciejewski et al. (2016), we used:

Q′? = 9PP−1 Mp

M?

(R?a

)5(ω? −

2π

P

)(7)

to estimate the tidal quality factor, where ω? is the stel-

lar rotation rate. Using Equation 9, we calculated a

tidal quality factor, Q′? = 1.219 × 105, consistent with

that reported by Maciejewski et al. (2016). Figure 11

shows the timing residuals of a linear ephemeris plotted

with the quadratic model, including our median fit with

1σ, 2σ, and 3σ levels shown in different transparencies.

Theoretical values are added for comparison.

Although the MCMC analysis is suggestive of period

decay, the result is consistent with zero within 1σ, as

seen in Figure 11. However, we can still provide a strong

constraint for the tidal quality factor in subgiants. We

report a 3σ upper limit of δP ≤ -5.17 × 10−8 days, or

a decay rate P ≤ -0.424 s yr−1. This corresponds to a

lower limit of Q′? ≥ 4.826 × 103 and thus clearly rules

out lower tidal quality factors suggested for subgiants

in the literature and places strong constraints on tidal

theories for evolved stars by effectively ruling out ∼2

orders of magnitude.

5.2. Spin-orbit Misalignment

Kepler-1658 is rapidly rotating, suggesting that it

started farther up the main-sequence than the Sun, with

a negligible or nonexistent convective envelope to ef-

fectively spin the star down through magnetic braking

(van Saders & Pinsonneault 2013). Solar-like oscilla-

tions are excited by near-surface convection, implying

that host star now has a convection zone. More specif-

ically, Kepler-1658 has Teff ≈ 6210 K, suggesting that

it recently crossed the transition between exoplanet sys-

tems showing small and large spin-orbit misalignments

(Winn et al. 2010). Therefore, Kepler-1658 may provide

valuable insights into the dynamical formation history

of hot Jupiters.

The obliquity, or the angle measured between the or-

bital angular momentum vector and rotational axis of

the star, is defined as:

cosψ = cos i? cos i+ sin i? sin i cosλ (8)

where λ is the sky-projected obliquity, i is the planet’s

inclination, and i? is the stellar inclination. The sky-

projected obliquity λ can be directly measured through

the Rossiter-McLaughlin (RM) effect for close-in giant

planets if that star is rotating fast enough (Rossiter

1924; McLaughlin 1924; Ohta et al. 2005; Winn et al.

2009). The planet’s inclination is trivially measured for

transiting systems.

The stellar inclination can be measured through rela-

tive amplitudes of rotationally split dipole modes (Gizon

& Solanki 2003). Stellar inclinations measured through

asteroseismology demand a long baseline to achieve suf-

ficient frequency resolution and SNR. The asteroseismic

technique has been applied to more than a handful of

exoplanet hosts (Huber et al. 2013b; Chaplin et al. 2013;

Davies et al. 2015; Campante et al. 2016a; Kamiaka et al.

2018), but is not applicable to Kepler-1658 due to the

low S/N.

Alternatively, the stellar spin inclination can be mea-

sured if there is evidence of rotational modulation (Winn

et al. 2007; Schlaufman 2010). More specifically, the re-

lation between the inclination, rotation period, and ro-

tational velocity is given by:

sin i? =

(Prot

2πR?

)v sin i . (9)

The detection of the rotational period in Kepler-1658

allows us to put constraints on the stellar inclination

through Equation (9). As discussed in Section 3.3, the

observed v sin i and rotation period imply i ≈ 90o. With

no prior information on the projected obliquity λ, the

true obliquity can range from 16.50o ≤ ψ ≤ 163.50o, pro-

viding tentative evidence for a spin-orbit misalignment.

Future spectroscopic observations while the planet is

15

transiting would allow further constraints on the true

obliquity. The expected signal of the RV anomaly due

to the RM effect through:

∆vRM ∼ v sin i

(RpR?

)2

(10)

yielding ∆vRM ∼ 55 m s−1 for KOI 4.01. The detection

of the RM effect would add Kepler-1658 to the small

number of systems for which true obliquity measure-

ments are possible (Benomar et al. 2014; Lund et al.

2014).

6. CONCLUSIONS

We have used asteroseismology and spectroscopy to

confirm Kepler-1658 b, Kepler’s first planet detection.

Our main conclusions can be summarized as follows:

• Kepler-1658 is a subgiant with Teff = 6216 ± 78

K, R? = 2.89 ± 0.12 R, and M?= 1.45 ± 0.06

M. As a massive subgiant, Kepler-1658 is cur-

rently undergoing a rapid phase of stellar evolu-

tion, joining only 9 known exoplanet hosts with

similar properties (15 including statistically vali-

dated planets).

• Kepler-1658 b is a hot Jupiter with Rp = 1.07

± 0.05 RJ and Mp = 5.73 ± 0.45 MJ, with an

orbital period of 3.85 days. The planet is part

of a small population of short-period (P . 100

days, a . 0.5 AU) planets around evolved (R? &2.5 R, log g . 3.7) stars. Sitting at an orbital

distance of only ≈ 0.05 AU, Kepler-1658 b is one

of the closest known planets to an evolved star.

We find tentative evidence for a mild eccentricity

(e = 0.06 ± 0.02), consistent with tidal evolution

studies suggesting moderate eccentricities of short-

period planets around evolved stars (Villaver &

Livio 2009; Grunblatt et al. 2018).

• Individual transit times over 4 years of Kepler ob-

servations place a strong upper limit of the orbital

period decay rate, P ≤ -0.42 s yr−1, setting a lower

limit on the tidal quality factor Q′? ≥ 4.826 × 103.

Our measurements provide the first strong obser-

vational limit on tidal quality factors of subgiant

stars, ruling out ∼2 orders of magnitude of sug-

gested theoretical values in the literature.

• Kepler-1658 sits close to the proposed misalign-

ment boundary of 6250 K for hot Jupiter obliq-

uities. While the combination of rotation period,

v sin i and stellar radius only provide tentative evi-

dence for a high obliquity (16.50o ≤ ψ ≤ 163.50o),

future spectroscopic observations of the RM ef-

fect may be able to provide stronger constraints

on obliquity damping and thus hot-Jupiter migra-

tion theories.

The Kepler field will be observed by the Transiting

Exoplanet Survey Satellite (TESS; Ricker et al. 2015)

in mid-2019. Extending the baseline of transit obser-

vations to over a decade for Kepler-1658 will allow for

a stronger constraint on orbital period decay in more

evolved systems. Extrapolating our period decay analy-

sis to the time Kepler-1658 would be observed by TESS

would rule out another order of magnitude for the tidal

quality factor in subgiant stars.

Kepler-1658 is typical of the asteroseimic host stars

we expect to find with TESS. Campante et al. (2016b)

estimated that TESS will find at least 100 asteroseismic

exoplanet hosts, and the first detection by Huber et al.

(2019) confirms that this yield with be biased towards

evolved subgiants similar to Kepler-1658 due to the in-

crease of asteroseismic detection probabilities with stel-

lar luminosity. Since targets found by TESS will be more

amenable to follow-up, we expect that larger samples of

short-period planets around evolved stars will provide

better clues into planet formation, tidal migration, and

dynamical evolution studies.

7. ACKNOWLEDGEMENTS

The authors thank Eric Gaidos, Josh Winn, Tom Bar-

clay, Jennifer van Saders, Lauren Weiss, Erik Petigura,

Benjamin J. Fulton, Cole Campbell Johnson, Sam Grun-

blatt, Jamie Tayar, Jessica Stasik, and Connor Auge for

helpful discussions. The authors wish to recognize and

acknowledge the very significant cultural role and rev-

erence that the summit of Maunakea has always had

within the indigenous Hawai‘ian community. We are

most fortunate to have the opportunity to conduct ob-

servations from this mountain.

A.C. acknowledges support by the National Science

Foundation under the Graduate Research Fellowship

Program. D.H. acknowledges support by the National

Aeronautics and Space Administration (NNX14AB92G,

NNX17AF76G, 80NSSC18K0362) and by the National

Science Foundation (AST-1717000). D.W.L. acknowl-

edges support from the Kepler mission under the Na-

tional Aeronautics and Space Administration Cooper-

ative Agreement (NNX13AABB58A) with the Smith-

soniann Astrophysical Observatory. T.L.C. acknowl-

edges support from the European Union’s Horizon 2020

research and innovation programme under the Marie

Sk lodowska-Curie grant number 792848. T.H. acknowl-

edges support by the Japan Society for Promotion of

Science under KAKENHI grant number JP16K17660.

16

Facilities: Keck:I (HIRES),. . . Software: astropy (Astropy Collaboration et al.

2013),emcee (Foreman-Mackeyetal. 2013b),Matplotlib

(Hunter 2007), Pandas (McKinney 2010), SciPy (Jones

et al. 2001–)

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